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moro69006
@moro69006
June 2021
1
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Je bloque :
Developper sin(x+h) et en deduire la limite quand h tend vers 0 du taux d'accroissement de [sin(x+h)-sin(x)]/h
Merci de m'expliquer!!
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danielwenin
Verified answer
[sin(x+h)-sin(x)]/h = (2sin(h/2.)cos(2x+h)/2)/h
lim
(2sin(h/2.)cos(2x+h)/2)/h = lim 2sin(h/2)/2.(h/2) . limcos(2x+h)/2)
= 1.cos(2x/2) = cosx
donc sin'x = cosx
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moro69006
oui mais ça c'est la preuve que cos (x) est la limite du taux d'accroissement qd h-->0 mais on part de sin (x+h). (pour arriver ensuite au taux d'accroissement), c'est ça que je n'arrive pas
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Le 2.9 s'il vous plait C'est avec l'heredite si quelqu'un pourrai m'expliquer
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Verified answer
[sin(x+h)-sin(x)]/h = (2sin(h/2.)cos(2x+h)/2)/hlim(2sin(h/2.)cos(2x+h)/2)/h = lim 2sin(h/2)/2.(h/2) . limcos(2x+h)/2)
= 1.cos(2x/2) = cosx
donc sin'x = cosx